Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_yellow 2 6.177490
beta0_yellow 2 2.736378
beta0_black 4 1.731138
beta1_black 11 1.597529
beta3_black 3 1.438833
beta1_pelagic 1 1.323761
beta2_black 5 1.301100
beta1_pH 8 1.295428
beta0_pH 3 1.286214
parameter n badRhat_avg
beta2_pelagic 3 1.262468
mu_beta0_yellow 1 1.255221
beta3_pH 1 1.187701
tau_beta0_yellow 1 1.181631
beta1_yellow 4 1.167240
beta2_yellow 2 1.163555
beta3_pelagic 1 1.151755
beta0_pelagic 1 1.147053
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0
beta0_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
beta0_pH 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0
beta0_yellow 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
beta1_black 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1
beta1_pelagic 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta1_pH 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0
beta1_yellow 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0
beta2_black 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0
beta2_pelagic 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0
beta2_yellow 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0
beta3_black 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0
beta3_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
beta3_pH 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
beta3_yellow 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
mu_beta0_yellow 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.130 0.072 -0.264 -0.132 0.019
mu_bc_H[2] -0.095 0.047 -0.172 -0.100 0.008
mu_bc_H[3] -0.438 0.070 -0.568 -0.441 -0.289
mu_bc_H[4] -0.998 0.193 -1.391 -0.992 -0.630
mu_bc_H[5] 0.941 0.963 -0.159 0.732 3.423
mu_bc_H[6] -2.155 0.314 -2.758 -2.161 -1.502
mu_bc_H[7] -0.468 0.112 -0.699 -0.466 -0.260
mu_bc_H[8] 0.235 0.346 -0.368 0.205 0.971
mu_bc_H[9] -0.296 0.133 -0.563 -0.295 -0.034
mu_bc_H[10] -0.109 0.069 -0.241 -0.111 0.041
mu_bc_H[11] -0.124 0.038 -0.197 -0.125 -0.051
mu_bc_H[12] -0.252 0.106 -0.478 -0.248 -0.048
mu_bc_H[13] -0.134 0.077 -0.282 -0.135 0.016
mu_bc_H[14] -0.305 0.097 -0.497 -0.301 -0.122
mu_bc_H[15] -0.341 0.050 -0.441 -0.342 -0.241
mu_bc_H[16] -0.259 0.383 -0.914 -0.294 0.582
mu_bc_R[1] 1.302 0.142 1.029 1.300 1.590
mu_bc_R[2] 1.452 0.095 1.261 1.455 1.631
mu_bc_R[3] 1.384 0.140 1.107 1.386 1.656
mu_bc_R[4] 0.922 0.202 0.504 0.934 1.280
mu_bc_R[5] 1.168 0.457 0.238 1.173 2.064
mu_bc_R[6] -1.596 0.414 -2.420 -1.591 -0.773
mu_bc_R[7] 0.301 0.190 -0.074 0.301 0.688
mu_bc_R[8] 0.547 0.198 0.151 0.555 0.920
mu_bc_R[9] 0.322 0.212 -0.136 0.339 0.689
mu_bc_R[10] 1.304 0.139 1.009 1.310 1.556
mu_bc_R[11] 1.041 0.100 0.840 1.040 1.233
mu_bc_R[12] 0.825 0.211 0.400 0.825 1.234
mu_bc_R[13] 1.024 0.100 0.820 1.026 1.223
mu_bc_R[14] 0.898 0.144 0.610 0.901 1.174
mu_bc_R[15] 0.781 0.110 0.560 0.784 0.996
mu_bc_R[16] 1.087 0.128 0.835 1.086 1.342
tau_pH[1] 5.302 0.455 4.446 5.293 6.194
tau_pH[2] 2.454 0.297 1.925 2.433 3.099
tau_pH[3] 2.244 0.223 1.837 2.237 2.704
beta0_pH[1,1] 0.512 0.179 0.143 0.514 0.850
beta0_pH[2,1] 1.335 0.181 0.965 1.338 1.685
beta0_pH[3,1] 1.412 0.189 0.988 1.428 1.751
beta0_pH[4,1] 1.566 0.208 1.110 1.579 1.934
beta0_pH[5,1] -0.858 0.298 -1.565 -0.837 -0.363
beta0_pH[6,1] -0.683 0.490 -1.880 -0.592 -0.008
beta0_pH[7,1] 0.243 0.654 -1.080 0.603 0.950
beta0_pH[8,1] -0.705 0.312 -1.467 -0.663 -0.215
beta0_pH[9,1] -0.647 0.297 -1.297 -0.616 -0.143
beta0_pH[10,1] 0.253 0.200 -0.157 0.258 0.634
beta0_pH[11,1] -0.079 0.164 -0.408 -0.073 0.228
beta0_pH[12,1] 0.497 0.186 0.132 0.502 0.850
beta0_pH[13,1] 0.011 0.142 -0.268 0.011 0.277
beta0_pH[14,1] -0.317 0.168 -0.659 -0.314 0.005
beta0_pH[15,1] -0.022 0.181 -0.392 -0.017 0.311
beta0_pH[16,1] -0.521 0.370 -1.361 -0.464 0.045
beta0_pH[1,2] 2.621 0.250 2.106 2.655 3.030
beta0_pH[2,2] 2.715 0.277 2.000 2.775 3.098
beta0_pH[3,2] 2.401 0.292 1.798 2.420 2.926
beta0_pH[4,2] 2.551 0.336 1.833 2.616 3.039
beta0_pH[5,2] 4.829 1.551 2.923 4.483 8.808
beta0_pH[6,2] 2.993 0.300 2.348 3.027 3.452
beta0_pH[7,2] 1.933 0.187 1.578 1.943 2.252
beta0_pH[8,2] 2.842 0.242 2.504 2.855 3.185
beta0_pH[9,2] 2.636 1.700 -2.368 3.300 3.780
beta0_pH[10,2] 3.690 0.301 3.308 3.709 4.090
beta0_pH[11,2] -4.854 0.299 -5.449 -4.848 -4.258
beta0_pH[12,2] -4.823 0.405 -5.652 -4.809 -4.080
beta0_pH[13,2] -4.592 0.400 -5.375 -4.596 -3.803
beta0_pH[14,2] -5.692 0.476 -6.669 -5.667 -4.818
beta0_pH[15,2] -4.243 0.326 -4.885 -4.241 -3.624
beta0_pH[16,2] -4.882 0.384 -5.675 -4.862 -4.149
beta0_pH[1,3] 0.519 0.592 -0.909 0.615 1.369
beta0_pH[2,3] 1.964 0.423 0.755 2.080 2.456
beta0_pH[3,3] 2.325 0.331 1.495 2.392 2.727
beta0_pH[4,3] 2.759 0.418 1.524 2.862 3.216
beta0_pH[5,3] 1.095 1.743 -1.723 0.847 5.367
beta0_pH[6,3] -0.760 1.152 -2.984 -0.857 1.509
beta0_pH[7,3] -2.194 0.645 -3.712 -2.127 -1.041
beta0_pH[8,3] 0.254 0.197 -0.143 0.259 0.621
beta0_pH[9,3] -0.968 0.808 -2.852 -0.758 0.234
beta0_pH[10,3] -0.308 1.019 -2.572 -0.095 1.073
beta0_pH[11,3] -0.154 0.330 -0.810 -0.159 0.506
beta0_pH[12,3] -0.870 0.348 -1.625 -0.843 -0.273
beta0_pH[13,3] -0.117 0.311 -0.708 -0.124 0.526
beta0_pH[14,3] -0.276 0.260 -0.783 -0.271 0.225
beta0_pH[15,3] -0.704 0.306 -1.327 -0.691 -0.148
beta0_pH[16,3] -0.381 0.289 -0.938 -0.380 0.172
beta1_pH[1,1] 3.125 0.325 2.553 3.099 3.795
beta1_pH[2,1] 2.194 0.281 1.693 2.171 2.791
beta1_pH[3,1] 2.026 0.305 1.505 2.000 2.708
beta1_pH[4,1] 2.409 0.349 1.875 2.366 3.208
beta1_pH[5,1] 2.278 0.357 1.697 2.245 3.088
beta1_pH[6,1] 3.945 1.194 2.331 3.706 6.900
beta1_pH[7,1] 2.347 1.499 0.312 2.233 5.648
beta1_pH[8,1] 4.239 1.113 2.646 4.028 6.999
beta1_pH[9,1] 2.325 0.417 1.678 2.279 3.264
beta1_pH[10,1] 2.359 0.275 1.833 2.352 2.915
beta1_pH[11,1] 3.265 0.205 2.892 3.254 3.689
beta1_pH[12,1] 2.538 0.219 2.108 2.538 2.969
beta1_pH[13,1] 2.971 0.213 2.575 2.965 3.399
beta1_pH[14,1] 3.422 0.221 3.012 3.417 3.867
beta1_pH[15,1] 2.526 0.222 2.118 2.517 2.981
beta1_pH[16,1] 4.235 0.683 3.225 4.138 5.785
beta1_pH[1,2] 2.953 8.601 0.005 1.013 24.474
beta1_pH[2,2] 7.849 26.239 0.006 0.964 105.453
beta1_pH[3,2] 1.201 0.461 0.575 1.180 1.878
beta1_pH[4,2] 6.325 32.814 0.089 1.019 49.494
beta1_pH[5,2] 0.180 1.052 0.000 0.001 1.586
beta1_pH[6,2] 0.562 1.959 0.000 0.003 2.917
beta1_pH[7,2] 0.066 0.266 0.000 0.001 0.793
beta1_pH[8,2] 0.094 0.552 0.000 0.001 0.793
beta1_pH[9,2] 0.871 1.751 0.000 0.004 5.795
beta1_pH[10,2] 3.831 9.483 0.000 0.005 35.045
beta1_pH[11,2] 6.712 0.324 6.070 6.704 7.353
beta1_pH[12,2] 6.540 0.488 5.664 6.505 7.606
beta1_pH[13,2] 7.014 0.438 6.187 7.009 7.889
beta1_pH[14,2] 7.350 0.492 6.459 7.325 8.360
beta1_pH[15,2] 6.750 0.352 6.066 6.745 7.447
beta1_pH[16,2] 7.514 0.412 6.733 7.498 8.352
beta1_pH[1,3] 3.066 1.197 1.601 2.753 6.377
beta1_pH[2,3] 0.594 1.280 0.000 0.183 3.381
beta1_pH[3,3] 0.377 0.837 0.000 0.088 2.354
beta1_pH[4,3] 0.652 1.893 0.000 0.096 4.749
beta1_pH[5,3] 3.762 2.348 1.648 3.246 9.391
beta1_pH[6,3] 3.069 6.380 1.123 2.671 5.145
beta1_pH[7,3] 3.045 0.651 1.919 2.982 4.550
beta1_pH[8,3] 2.840 0.389 2.146 2.819 3.635
beta1_pH[9,3] 3.048 0.806 1.838 2.877 5.008
beta1_pH[10,3] 3.723 1.093 2.216 3.494 6.176
beta1_pH[11,3] 2.758 0.382 2.021 2.755 3.518
beta1_pH[12,3] 4.130 0.432 3.340 4.102 5.048
beta1_pH[13,3] 1.694 0.335 0.982 1.712 2.320
beta1_pH[14,3] 2.505 0.332 1.866 2.506 3.161
beta1_pH[15,3] 1.991 0.332 1.361 1.987 2.660
beta1_pH[16,3] 1.777 0.324 1.173 1.773 2.429
beta2_pH[1,1] 0.468 0.117 0.288 0.455 0.731
beta2_pH[2,1] 0.557 0.263 0.242 0.507 1.213
beta2_pH[3,1] 0.601 0.368 0.216 0.526 1.489
beta2_pH[4,1] 0.462 0.175 0.213 0.437 0.860
beta2_pH[5,1] 1.571 1.258 0.249 1.293 4.808
beta2_pH[6,1] 0.185 0.067 0.085 0.174 0.347
beta2_pH[7,1] -0.703 1.720 -5.169 0.017 1.391
beta2_pH[8,1] 0.233 0.090 0.115 0.216 0.441
beta2_pH[9,1] 0.443 0.241 0.173 0.400 0.965
beta2_pH[10,1] 0.648 0.408 0.306 0.575 1.408
beta2_pH[11,1] 0.793 0.211 0.481 0.759 1.298
beta2_pH[12,1] 1.379 0.517 0.750 1.276 2.645
beta2_pH[13,1] 0.741 0.227 0.415 0.704 1.287
beta2_pH[14,1] 0.838 0.216 0.531 0.800 1.320
beta2_pH[15,1] 0.812 0.296 0.417 0.760 1.547
beta2_pH[16,1] 0.350 0.163 0.167 0.301 0.780
beta2_pH[1,2] -1.549 4.161 -9.830 -1.579 6.428
beta2_pH[2,2] -2.702 3.913 -10.651 -2.721 5.439
beta2_pH[3,2] -3.902 2.707 -10.787 -3.258 -0.677
beta2_pH[4,2] -3.693 2.876 -10.695 -3.044 -0.178
beta2_pH[5,2] -0.914 4.299 -9.123 -1.069 8.076
beta2_pH[6,2] -1.143 4.237 -9.324 -1.305 7.838
beta2_pH[7,2] -0.837 4.356 -9.065 -1.007 8.013
beta2_pH[8,2] -0.943 4.406 -9.490 -1.200 7.855
beta2_pH[9,2] -0.746 4.437 -9.175 -1.089 8.290
beta2_pH[10,2] -1.321 4.459 -9.595 -1.670 8.153
beta2_pH[11,2] -7.013 2.340 -12.825 -6.620 -3.686
beta2_pH[12,2] -4.235 2.629 -9.970 -3.912 -0.762
beta2_pH[13,2] -4.360 2.441 -10.166 -3.737 -1.446
beta2_pH[14,2] -5.417 2.400 -11.056 -4.975 -2.115
beta2_pH[15,2] -6.856 2.519 -13.327 -6.320 -3.344
beta2_pH[16,2] -7.102 2.522 -13.630 -6.631 -3.634
beta2_pH[1,3] 1.455 2.058 0.129 0.476 7.321
beta2_pH[2,3] 1.047 3.441 -6.330 0.827 8.082
beta2_pH[3,3] 0.583 3.581 -6.857 0.433 8.565
beta2_pH[4,3] 0.745 3.550 -7.013 0.598 8.290
beta2_pH[5,3] 3.521 2.992 -0.197 2.954 10.707
beta2_pH[6,3] 3.514 3.043 -0.074 2.917 10.821
beta2_pH[7,3] 3.410 2.730 0.495 2.643 10.285
beta2_pH[8,3] 4.897 2.967 0.735 4.477 11.938
beta2_pH[9,3] 2.999 2.810 0.293 2.221 9.860
beta2_pH[10,3] 2.247 2.616 0.296 0.821 8.888
beta2_pH[11,3] -1.993 1.438 -6.116 -1.617 -0.597
beta2_pH[12,3] -2.149 1.284 -5.817 -1.805 -0.937
beta2_pH[13,3] -2.642 1.785 -7.538 -2.074 -0.800
beta2_pH[14,3] -2.559 1.619 -7.327 -2.077 -0.905
beta2_pH[15,3] -2.728 1.818 -7.888 -2.186 -1.015
beta2_pH[16,3] -2.773 1.833 -8.054 -2.169 -0.894
beta3_pH[1,1] 35.827 0.838 34.242 35.789 37.568
beta3_pH[2,1] 33.444 1.131 31.423 33.376 35.902
beta3_pH[3,1] 33.823 1.093 31.864 33.781 36.107
beta3_pH[4,1] 33.928 1.250 31.689 33.861 36.543
beta3_pH[5,1] 27.759 1.185 26.385 27.487 31.244
beta3_pH[6,1] 38.908 3.215 32.902 38.739 45.156
beta3_pH[7,1] 28.541 9.746 18.371 23.861 45.657
beta3_pH[8,1] 40.310 2.255 36.533 40.035 45.260
beta3_pH[9,1] 30.618 1.574 27.936 30.531 33.780
beta3_pH[10,1] 32.700 0.909 30.936 32.665 34.593
beta3_pH[11,1] 30.431 0.463 29.578 30.399 31.514
beta3_pH[12,1] 30.192 0.393 29.397 30.204 30.960
beta3_pH[13,1] 33.248 0.577 32.150 33.236 34.406
beta3_pH[14,1] 32.041 0.449 31.179 32.029 32.977
beta3_pH[15,1] 31.245 0.664 29.965 31.202 32.648
beta3_pH[16,1] 32.203 1.065 30.386 32.060 34.637
beta3_pH[1,2] 31.174 8.869 18.411 29.097 44.286
beta3_pH[2,2] 24.676 6.455 18.220 22.051 42.975
beta3_pH[3,2] 41.745 1.748 39.547 41.897 44.044
beta3_pH[4,2] 33.632 8.626 19.417 38.248 44.388
beta3_pH[5,2] 29.843 8.073 18.578 28.742 45.128
beta3_pH[6,2] 30.973 7.463 18.639 32.020 44.921
beta3_pH[7,2] 29.838 7.867 18.462 28.975 44.917
beta3_pH[8,2] 29.611 7.792 18.490 28.628 44.704
beta3_pH[9,2] 31.091 8.641 18.545 28.537 45.423
beta3_pH[10,2] 29.349 6.825 18.535 29.136 44.301
beta3_pH[11,2] 43.388 0.147 43.143 43.375 43.706
beta3_pH[12,2] 43.191 0.196 42.759 43.183 43.587
beta3_pH[13,2] 43.824 0.146 43.473 43.848 44.049
beta3_pH[14,2] 43.316 0.162 43.080 43.289 43.688
beta3_pH[15,2] 43.399 0.162 43.136 43.381 43.752
beta3_pH[16,2] 43.497 0.164 43.197 43.493 43.811
beta3_pH[1,3] 38.624 2.252 33.962 39.078 43.156
beta3_pH[2,3] 30.727 7.750 18.472 30.904 44.991
beta3_pH[3,3] 30.253 8.287 18.484 29.479 45.056
beta3_pH[4,3] 28.634 7.865 18.422 26.815 44.794
beta3_pH[5,3] 26.402 6.586 18.302 24.848 42.541
beta3_pH[6,3] 27.081 6.534 18.678 25.693 44.374
beta3_pH[7,3] 26.461 0.998 24.695 26.357 28.744
beta3_pH[8,3] 41.503 0.368 40.880 41.490 42.203
beta3_pH[9,3] 32.414 1.854 27.709 33.225 34.368
beta3_pH[10,3] 34.607 1.587 31.374 34.915 36.718
beta3_pH[11,3] 41.751 0.793 40.145 41.764 43.284
beta3_pH[12,3] 41.727 0.386 40.976 41.742 42.467
beta3_pH[13,3] 42.734 0.873 41.125 42.733 44.661
beta3_pH[14,3] 41.114 0.547 39.987 41.114 42.163
beta3_pH[15,3] 42.585 0.633 41.206 42.656 43.671
beta3_pH[16,3] 42.851 0.739 41.192 42.961 44.097
beta0_pelagic[1] 1.947 0.453 0.693 2.097 2.412
beta0_pelagic[2] 1.366 0.294 0.425 1.435 1.716
beta0_pelagic[3] 0.199 0.364 -0.770 0.261 0.736
beta0_pelagic[4] 0.214 0.489 -1.039 0.286 1.002
beta0_pelagic[5] 0.594 1.203 -2.928 1.082 1.492
beta0_pelagic[6] 1.274 0.397 0.203 1.388 1.708
beta0_pelagic[7] 1.584 0.147 1.297 1.591 1.847
beta0_pelagic[8] 1.715 0.144 1.428 1.718 1.979
beta0_pelagic[9] 2.377 0.557 1.010 2.589 2.966
beta0_pelagic[10] 2.537 0.180 2.168 2.553 2.806
beta0_pelagic[11] -0.115 0.463 -1.310 -0.096 0.625
beta0_pelagic[12] 1.685 0.135 1.423 1.686 1.957
beta0_pelagic[13] 0.306 0.199 -0.146 0.323 0.647
beta0_pelagic[14] -0.152 0.288 -0.814 -0.130 0.326
beta0_pelagic[15] -0.270 0.133 -0.524 -0.271 -0.009
beta0_pelagic[16] 0.188 0.318 -0.541 0.271 0.621
beta1_pelagic[1] 0.307 0.467 0.000 0.077 1.623
beta1_pelagic[2] 0.207 0.332 0.000 0.057 1.268
beta1_pelagic[3] 0.897 0.511 0.155 0.788 2.170
beta1_pelagic[4] 0.973 0.521 0.011 0.917 2.257
beta1_pelagic[5] 0.620 1.289 0.000 0.001 4.368
beta1_pelagic[6] 0.268 0.496 0.000 0.002 1.543
beta1_pelagic[7] 1.041 5.312 0.000 0.001 12.673
beta1_pelagic[8] 0.061 0.230 0.000 0.001 0.564
beta1_pelagic[9] 0.437 0.660 0.000 0.008 1.978
beta1_pelagic[10] 0.093 0.389 0.000 0.001 0.881
beta1_pelagic[11] 4.115 1.008 2.439 4.028 6.301
beta1_pelagic[12] 2.806 0.300 2.214 2.797 3.393
beta1_pelagic[13] 2.949 0.731 1.757 2.881 4.585
beta1_pelagic[14] 4.546 1.051 2.943 4.395 6.963
beta1_pelagic[15] 2.951 0.254 2.441 2.960 3.437
beta1_pelagic[16] 3.917 1.069 2.755 3.492 6.718
beta2_pelagic[1] 2.104 3.266 -5.087 1.816 9.059
beta2_pelagic[2] 2.273 3.060 -3.749 1.862 9.050
beta2_pelagic[3] 2.247 2.280 0.087 1.536 8.031
beta2_pelagic[4] 2.688 2.533 0.166 1.929 9.567
beta2_pelagic[5] 0.540 4.503 -7.998 0.549 9.030
beta2_pelagic[6] 1.773 4.213 -7.304 1.855 9.690
beta2_pelagic[7] 0.723 4.609 -8.933 0.809 9.617
beta2_pelagic[8] 1.018 4.392 -7.750 1.040 9.245
beta2_pelagic[9] 2.452 4.231 -7.060 2.780 8.426
beta2_pelagic[10] 1.158 4.450 -7.901 1.328 9.378
beta2_pelagic[11] 0.570 1.279 0.112 0.201 4.715
beta2_pelagic[12] 4.089 2.220 1.202 3.590 9.457
beta2_pelagic[13] 0.710 0.913 0.190 0.451 3.077
beta2_pelagic[14] 0.294 0.117 0.149 0.272 0.582
beta2_pelagic[15] 4.299 2.224 1.303 3.867 9.906
beta2_pelagic[16] 2.169 2.514 0.173 1.054 8.644
beta3_pelagic[1] 27.414 7.713 18.347 24.578 44.834
beta3_pelagic[2] 29.103 8.162 18.350 27.296 45.104
beta3_pelagic[3] 30.081 4.620 22.804 29.794 42.477
beta3_pelagic[4] 25.860 3.570 20.738 25.603 38.017
beta3_pelagic[5] 32.587 9.560 18.687 31.532 45.984
beta3_pelagic[6] 30.660 7.251 18.723 30.143 44.712
beta3_pelagic[7] 29.264 8.080 18.469 28.084 44.929
beta3_pelagic[8] 29.616 8.025 18.532 28.133 44.928
beta3_pelagic[9] 29.752 6.980 18.788 28.419 44.380
beta3_pelagic[10] 29.345 8.194 18.355 27.873 44.777
beta3_pelagic[11] 42.179 2.315 36.089 42.616 45.682
beta3_pelagic[12] 43.454 0.256 43.005 43.447 43.945
beta3_pelagic[13] 42.846 1.292 40.420 42.784 45.449
beta3_pelagic[14] 42.502 1.750 38.684 42.541 45.683
beta3_pelagic[15] 43.148 0.241 42.554 43.167 43.576
beta3_pelagic[16] 43.029 0.995 40.646 43.144 45.311
mu_beta0_pelagic[1] 0.882 0.812 -0.854 0.905 2.546
mu_beta0_pelagic[2] 1.651 0.586 0.192 1.731 2.614
mu_beta0_pelagic[3] 0.273 0.484 -0.729 0.290 1.248
tau_beta0_pelagic[1] 1.204 2.726 0.061 0.635 5.255
tau_beta0_pelagic[2] 1.973 2.949 0.100 1.370 6.615
tau_beta0_pelagic[3] 1.433 1.134 0.161 1.151 4.389
beta0_yellow[1] -0.551 0.190 -0.999 -0.531 -0.245
beta0_yellow[2] 0.488 0.180 0.101 0.502 0.793
beta0_yellow[3] -0.326 0.266 -0.804 -0.300 0.032
beta0_yellow[4] 0.813 0.278 0.028 0.861 1.195
beta0_yellow[5] -1.229 0.423 -2.046 -1.229 -0.404
beta0_yellow[6] 0.277 0.217 -0.165 0.278 0.699
beta0_yellow[7] 0.901 0.546 -0.881 1.028 1.340
beta0_yellow[8] 0.698 0.652 -1.131 0.928 1.285
beta0_yellow[9] -0.101 0.307 -0.673 -0.096 0.466
beta0_yellow[10] 0.233 0.153 -0.058 0.235 0.518
beta0_yellow[11] -1.485 0.935 -2.816 -1.812 0.036
beta0_yellow[12] -3.668 0.419 -4.552 -3.649 -2.881
beta0_yellow[13] -3.791 0.467 -4.796 -3.756 -2.961
beta0_yellow[14] -2.112 0.506 -3.069 -2.132 -1.032
beta0_yellow[15] -2.891 0.433 -3.786 -2.882 -2.079
beta0_yellow[16] -2.416 0.475 -3.352 -2.423 -1.468
beta1_yellow[1] 0.495 0.982 0.000 0.309 1.818
beta1_yellow[2] 1.096 0.428 0.575 1.033 2.101
beta1_yellow[3] 0.692 0.477 0.024 0.658 1.377
beta1_yellow[4] 1.445 0.835 0.636 1.210 4.054
beta1_yellow[5] 3.141 1.891 1.363 2.876 6.635
beta1_yellow[6] 2.266 0.351 1.577 2.262 2.968
beta1_yellow[7] 7.310 8.351 1.014 4.233 33.544
beta1_yellow[8] 2.188 2.481 0.020 1.739 8.504
beta1_yellow[9] 1.597 0.520 0.793 1.560 2.690
beta1_yellow[10] 2.333 0.458 1.518 2.316 3.279
beta1_yellow[11] 2.083 0.606 0.750 2.143 3.167
beta1_yellow[12] 2.474 0.434 1.681 2.448 3.384
beta1_yellow[13] 2.908 0.470 2.065 2.877 3.884
beta1_yellow[14] 2.187 0.503 1.120 2.208 3.115
beta1_yellow[15] 2.134 0.434 1.322 2.125 3.019
beta1_yellow[16] 2.173 0.474 1.226 2.177 3.108
beta2_yellow[1] -2.368 2.816 -9.113 -1.820 2.522
beta2_yellow[2] -2.737 2.436 -9.314 -2.033 -0.154
beta2_yellow[3] -2.341 2.158 -8.452 -1.780 -0.099
beta2_yellow[4] -2.289 2.447 -8.565 -1.518 -0.092
beta2_yellow[5] -4.276 2.873 -11.071 -3.705 -0.517
beta2_yellow[6] 3.627 2.257 0.909 2.999 9.472
beta2_yellow[7] -4.221 3.601 -11.429 -4.178 4.578
beta2_yellow[8] -2.356 4.336 -11.114 -2.150 6.786
beta2_yellow[9] 3.663 2.591 0.178 3.284 9.623
beta2_yellow[10] -4.585 2.864 -11.476 -4.046 -0.766
beta2_yellow[11] -3.301 2.065 -8.278 -3.050 -0.148
beta2_yellow[12] -3.979 1.951 -8.798 -3.616 -1.205
beta2_yellow[13] -3.929 1.856 -8.524 -3.575 -1.431
beta2_yellow[14] -3.986 2.117 -9.307 -3.604 -0.874
beta2_yellow[15] -3.496 1.870 -8.407 -3.258 -1.048
beta2_yellow[16] -3.997 2.143 -9.494 -3.551 -1.240
beta3_yellow[1] 27.808 7.845 18.338 25.294 44.721
beta3_yellow[2] 29.096 2.018 24.729 28.934 33.025
beta3_yellow[3] 33.067 3.479 24.079 32.981 41.553
beta3_yellow[4] 29.089 3.697 20.657 28.161 36.046
beta3_yellow[5] 33.294 1.516 30.047 33.383 35.607
beta3_yellow[6] 39.682 0.537 38.737 39.643 40.868
beta3_yellow[7] 20.604 2.683 18.517 20.049 28.496
beta3_yellow[8] 25.170 5.914 18.225 24.070 43.515
beta3_yellow[9] 37.693 2.360 35.867 37.593 42.928
beta3_yellow[10] 29.334 0.636 27.876 29.428 30.120
beta3_yellow[11] 40.526 6.954 28.571 45.091 45.965
beta3_yellow[12] 43.359 0.419 42.598 43.323 44.231
beta3_yellow[13] 44.858 0.369 44.039 44.919 45.478
beta3_yellow[14] 44.275 0.974 43.099 44.260 45.851
beta3_yellow[15] 45.200 0.517 44.117 45.213 45.967
beta3_yellow[16] 44.608 0.633 43.442 44.594 45.807
mu_beta0_yellow[1] 0.095 0.560 -1.046 0.087 1.213
mu_beta0_yellow[2] 0.106 0.493 -0.934 0.121 1.071
mu_beta0_yellow[3] -2.328 0.737 -3.504 -2.440 -0.544
tau_beta0_yellow[1] 1.888 3.071 0.095 1.139 7.686
tau_beta0_yellow[2] 1.342 1.330 0.131 0.987 4.578
tau_beta0_yellow[3] 1.216 2.045 0.078 0.676 5.069
beta0_black[1] 0.006 0.194 -0.360 0.002 0.389
beta0_black[2] 1.910 0.134 1.673 1.911 2.155
beta0_black[3] 1.312 0.131 1.056 1.314 1.563
beta0_black[4] 2.214 0.277 1.658 2.251 2.641
beta0_black[5] 1.679 2.077 -2.893 1.675 6.127
beta0_black[6] 1.618 2.077 -3.075 1.652 5.771
beta0_black[7] 1.739 2.094 -2.741 1.716 6.412
beta0_black[8] 1.282 0.223 0.853 1.285 1.709
beta0_black[9] 2.435 0.245 1.951 2.440 2.896
beta0_black[10] 1.467 0.134 1.210 1.466 1.736
beta0_black[11] 3.478 0.161 3.165 3.478 3.777
beta0_black[12] 4.610 0.256 4.143 4.593 5.105
beta0_black[13] -0.096 0.222 -0.544 -0.088 0.331
beta0_black[14] 2.558 0.539 0.975 2.702 3.094
beta0_black[15] 1.282 0.167 0.969 1.290 1.585
beta0_black[16] 4.227 0.357 3.827 4.261 4.568
beta2_black[1] 1.987 2.991 -4.650 2.004 8.370
beta2_black[2] 0.050 3.342 -6.750 0.046 6.816
beta2_black[3] -0.190 3.306 -7.745 0.076 6.270
beta2_black[4] -1.158 3.099 -7.623 -1.064 5.505
beta2_black[5] 0.066 3.218 -6.269 -0.017 6.871
beta2_black[6] 0.003 3.228 -7.043 0.011 6.924
beta2_black[7] 0.041 3.184 -6.562 0.056 6.983
beta2_black[8] 0.027 3.264 -6.795 0.018 7.013
beta2_black[9] -0.006 3.166 -6.517 -0.042 6.700
beta2_black[10] 0.003 3.252 -6.577 -0.077 7.210
beta2_black[11] -1.024 2.323 -5.313 -0.993 3.510
beta2_black[12] -1.834 2.482 -6.682 -1.844 4.218
beta2_black[13] -2.053 1.578 -6.507 -1.546 -0.474
beta2_black[14] -1.252 2.453 -6.734 -1.061 3.973
beta2_black[15] -0.989 2.760 -6.818 -1.158 5.214
beta2_black[16] -0.967 2.768 -6.890 -1.039 4.904
beta3_black[1] 38.026 6.912 19.772 41.371 43.524
beta3_black[2] 30.193 8.093 18.529 29.270 44.883
beta3_black[3] 30.193 8.008 18.513 29.257 44.823
beta3_black[4] 31.876 5.955 19.206 32.637 43.939
beta3_black[5] 30.204 8.076 18.422 29.261 45.019
beta3_black[6] 30.174 7.923 18.578 29.352 44.914
beta3_black[7] 30.381 8.027 18.451 29.791 44.917
beta3_black[8] 29.994 8.025 18.505 28.868 44.848
beta3_black[9] 29.908 7.928 18.367 28.958 44.903
beta3_black[10] 29.865 8.000 18.465 28.792 44.936
beta3_black[11] 31.119 7.829 18.601 31.061 45.000
beta3_black[12] 32.087 4.868 19.391 32.821 43.306
beta3_black[13] 39.248 0.719 37.580 39.320 40.442
beta3_black[14] 34.755 7.065 19.015 37.037 44.878
beta3_black[15] 30.859 7.923 18.554 30.515 44.960
beta3_black[16] 31.084 7.816 18.639 30.946 44.766
beta4_black[1] -0.264 0.189 -0.635 -0.261 0.092
beta4_black[2] 0.242 0.178 -0.112 0.244 0.577
beta4_black[3] -0.933 0.187 -1.302 -0.934 -0.577
beta4_black[4] 0.488 0.230 0.050 0.488 0.929
beta4_black[5] 0.234 2.718 -4.444 0.126 5.368
beta4_black[6] 0.282 2.460 -4.384 0.160 5.454
beta4_black[7] 0.211 2.383 -4.192 0.154 4.896
beta4_black[8] -0.693 0.366 -1.397 -0.700 -0.001
beta4_black[9] 1.476 1.015 -0.132 1.336 3.831
beta4_black[10] 0.022 0.185 -0.336 0.022 0.397
beta4_black[11] -0.705 0.208 -1.112 -0.704 -0.304
beta4_black[12] 0.254 0.340 -0.409 0.247 0.932
beta4_black[13] -1.201 0.213 -1.619 -1.205 -0.780
beta4_black[14] -0.166 0.234 -0.613 -0.167 0.305
beta4_black[15] -0.894 0.207 -1.300 -0.894 -0.491
beta4_black[16] -0.598 0.225 -1.052 -0.600 -0.156
mu_beta0_black[1] 1.338 0.964 -0.613 1.343 3.304
mu_beta0_black[2] 1.683 1.002 -0.449 1.693 3.779
mu_beta0_black[3] 2.633 1.034 0.494 2.651 4.644
tau_beta0_black[1] 0.728 0.722 0.052 0.488 2.636
tau_beta0_black[2] 1.969 3.902 0.053 0.807 10.493
tau_beta0_black[3] 0.248 0.165 0.052 0.206 0.674
beta0_dsr[11] -2.918 0.282 -3.455 -2.927 -2.359
beta0_dsr[12] 4.525 0.279 3.983 4.527 5.082
beta0_dsr[13] -1.351 0.314 -1.961 -1.338 -0.793
beta0_dsr[14] -3.665 0.490 -4.643 -3.668 -2.700
beta0_dsr[15] -1.939 0.274 -2.484 -1.947 -1.424
beta0_dsr[16] -2.982 0.355 -3.709 -2.974 -2.288
beta1_dsr[11] 4.851 0.291 4.272 4.852 5.428
beta1_dsr[12] 6.390 5.909 2.250 5.016 19.078
beta1_dsr[13] 2.872 0.373 2.289 2.850 3.518
beta1_dsr[14] 6.331 0.517 5.304 6.324 7.380
beta1_dsr[15] 3.334 0.278 2.789 3.335 3.869
beta1_dsr[16] 5.807 0.372 5.087 5.795 6.565
beta2_dsr[11] -8.225 2.241 -13.459 -7.892 -4.665
beta2_dsr[12] -7.011 2.575 -12.688 -6.905 -2.417
beta2_dsr[13] -6.346 2.708 -12.225 -6.329 -1.455
beta2_dsr[14] -6.074 2.669 -11.825 -5.969 -1.871
beta2_dsr[15] -7.712 2.391 -13.370 -7.367 -3.742
beta2_dsr[16] -7.899 2.328 -13.513 -7.576 -4.298
beta3_dsr[11] 43.494 0.150 43.223 43.491 43.779
beta3_dsr[12] 33.970 0.725 32.093 34.114 34.808
beta3_dsr[13] 43.238 0.310 42.807 43.183 43.845
beta3_dsr[14] 43.335 0.223 43.079 43.272 43.900
beta3_dsr[15] 43.513 0.185 43.170 43.512 43.848
beta3_dsr[16] 43.436 0.156 43.174 43.425 43.760
beta4_dsr[11] 0.586 0.211 0.174 0.583 1.011
beta4_dsr[12] 0.249 0.434 -0.648 0.252 1.068
beta4_dsr[13] -0.176 0.212 -0.592 -0.176 0.227
beta4_dsr[14] 0.146 0.242 -0.315 0.146 0.609
beta4_dsr[15] 0.727 0.212 0.313 0.728 1.142
beta4_dsr[16] 0.138 0.229 -0.312 0.142 0.587
beta0_slope[11] -1.944 0.162 -2.265 -1.941 -1.638
beta0_slope[12] -4.650 0.262 -5.181 -4.650 -4.141
beta0_slope[13] -1.339 0.204 -1.781 -1.323 -0.984
beta0_slope[14] -2.640 0.178 -2.981 -2.640 -2.289
beta0_slope[15] -1.370 0.163 -1.691 -1.365 -1.057
beta0_slope[16] -2.725 0.168 -3.058 -2.730 -2.416
beta1_slope[11] 4.591 0.295 4.040 4.590 5.176
beta1_slope[12] 5.005 0.517 4.018 4.996 6.037
beta1_slope[13] 2.903 0.484 2.241 2.833 4.243
beta1_slope[14] 6.521 0.543 5.484 6.499 7.606
beta1_slope[15] 3.056 0.281 2.506 3.050 3.612
beta1_slope[16] 5.376 0.395 4.646 5.364 6.174
beta2_slope[11] 7.962 2.316 4.376 7.663 13.380
beta2_slope[12] 7.096 2.430 2.849 6.864 12.364
beta2_slope[13] 5.716 2.918 0.411 5.759 11.578
beta2_slope[14] 6.496 2.400 2.431 6.300 11.710
beta2_slope[15] 7.487 2.305 3.692 7.203 12.801
beta2_slope[16] 7.617 2.363 3.899 7.302 13.084
beta3_slope[11] 43.471 0.151 43.196 43.467 43.770
beta3_slope[12] 43.408 0.230 43.058 43.382 43.877
beta3_slope[13] 43.634 0.432 42.903 43.709 44.292
beta3_slope[14] 43.321 0.172 43.096 43.278 43.770
beta3_slope[15] 43.517 0.194 43.167 43.520 43.873
beta3_slope[16] 43.454 0.167 43.170 43.443 43.790
beta4_slope[11] -0.572 0.213 -0.979 -0.571 -0.146
beta4_slope[12] -1.423 0.660 -2.896 -1.346 -0.359
beta4_slope[13] 0.053 0.223 -0.369 0.051 0.493
beta4_slope[14] -0.175 0.261 -0.688 -0.179 0.357
beta4_slope[15] -0.728 0.211 -1.149 -0.723 -0.323
beta4_slope[16] -0.189 0.230 -0.635 -0.193 0.266
sigma_H[1] 0.200 0.053 0.105 0.198 0.307
sigma_H[2] 0.171 0.031 0.118 0.168 0.237
sigma_H[3] 0.196 0.043 0.119 0.193 0.289
sigma_H[4] 0.417 0.078 0.292 0.409 0.587
sigma_H[5] 0.996 0.207 0.630 0.984 1.442
sigma_H[6] 0.391 0.199 0.036 0.388 0.811
sigma_H[7] 0.298 0.059 0.208 0.291 0.440
sigma_H[8] 0.417 0.095 0.269 0.407 0.614
sigma_H[9] 0.527 0.125 0.332 0.511 0.809
sigma_H[10] 0.215 0.043 0.140 0.212 0.305
sigma_H[11] 0.278 0.045 0.201 0.273 0.381
sigma_H[12] 0.436 0.168 0.208 0.409 0.781
sigma_H[13] 0.215 0.038 0.149 0.213 0.298
sigma_H[14] 0.508 0.091 0.345 0.501 0.705
sigma_H[15] 0.248 0.041 0.178 0.244 0.336
sigma_H[16] 0.223 0.044 0.152 0.217 0.328
lambda_H[1] 3.161 3.930 0.151 1.776 14.168
lambda_H[2] 8.137 7.221 0.835 6.012 28.423
lambda_H[3] 5.887 8.984 0.249 3.038 29.657
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 4.402 9.534 0.038 1.147 33.481
lambda_H[6] 6.856 13.193 0.008 0.832 43.120
lambda_H[7] 0.013 0.010 0.002 0.011 0.038
lambda_H[8] 8.492 10.887 0.137 4.751 37.292
lambda_H[9] 0.015 0.010 0.003 0.012 0.041
lambda_H[10] 0.322 0.671 0.037 0.205 1.153
lambda_H[11] 0.251 0.339 0.011 0.126 1.198
lambda_H[12] 4.758 6.187 0.186 2.729 21.316
lambda_H[13] 3.472 3.206 0.245 2.554 11.525
lambda_H[14] 3.391 4.118 0.228 2.052 14.906
lambda_H[15] 0.026 0.048 0.004 0.016 0.108
lambda_H[16] 0.783 1.091 0.040 0.405 3.777
mu_lambda_H[1] 4.327 1.877 1.286 4.096 8.294
mu_lambda_H[2] 3.850 1.940 0.652 3.692 8.001
mu_lambda_H[3] 3.491 1.868 0.761 3.241 7.821
sigma_lambda_H[1] 8.518 4.283 2.102 7.844 18.147
sigma_lambda_H[2] 8.371 4.627 1.099 7.789 18.374
sigma_lambda_H[3] 6.284 4.063 0.955 5.427 16.538
beta_H[1,1] 6.929 1.082 4.390 7.118 8.535
beta_H[2,1] 9.870 0.499 8.843 9.896 10.789
beta_H[3,1] 8.009 0.773 6.110 8.087 9.293
beta_H[4,1] 9.422 7.785 -6.384 9.483 24.087
beta_H[5,1] 0.161 2.248 -4.802 0.344 4.115
beta_H[6,1] 3.115 4.001 -6.965 4.481 7.834
beta_H[7,1] 0.719 5.897 -12.059 1.268 10.679
beta_H[8,1] 1.446 4.349 -2.250 1.226 3.628
beta_H[9,1] 13.092 5.549 2.172 13.103 23.964
beta_H[10,1] 7.089 1.651 3.697 7.146 10.223
beta_H[11,1] 5.091 3.505 -2.879 5.804 9.947
beta_H[12,1] 2.635 1.132 0.699 2.584 4.949
beta_H[13,1] 9.041 0.984 7.197 9.119 10.516
beta_H[14,1] 2.229 0.985 0.258 2.226 4.240
beta_H[15,1] -6.149 3.847 -12.799 -6.418 2.545
beta_H[16,1] 3.556 2.673 -0.787 3.204 9.916
beta_H[1,2] 7.909 0.244 7.428 7.916 8.379
beta_H[2,2] 10.022 0.135 9.757 10.024 10.288
beta_H[3,2] 8.953 0.198 8.564 8.952 9.345
beta_H[4,2] 3.566 1.461 0.844 3.494 6.631
beta_H[5,2] 1.955 0.922 0.120 1.992 3.695
beta_H[6,2] 5.702 1.027 3.312 5.873 7.233
beta_H[7,2] 2.576 1.143 0.519 2.521 5.030
beta_H[8,2] 3.013 1.180 1.481 3.147 4.255
beta_H[9,2] 3.524 1.106 1.429 3.469 5.833
beta_H[10,2] 8.208 0.344 7.485 8.225 8.855
beta_H[11,2] 9.775 0.632 8.841 9.658 11.194
beta_H[12,2] 3.951 0.375 3.251 3.942 4.706
beta_H[13,2] 9.121 0.255 8.685 9.107 9.612
beta_H[14,2] 4.030 0.355 3.338 4.032 4.716
beta_H[15,2] 11.369 0.689 9.904 11.400 12.599
beta_H[16,2] 4.538 0.788 3.091 4.516 6.160
beta_H[1,3] 8.460 0.235 8.026 8.449 8.951
beta_H[2,3] 10.066 0.118 9.831 10.067 10.302
beta_H[3,3] 9.619 0.162 9.308 9.617 9.952
beta_H[4,3] -2.472 0.901 -4.270 -2.470 -0.691
beta_H[5,3] 3.814 0.594 2.609 3.813 4.946
beta_H[6,3] 8.009 1.197 6.380 7.627 10.567
beta_H[7,3] -2.656 0.756 -4.126 -2.667 -1.215
beta_H[8,3] 5.247 0.536 4.641 5.183 6.207
beta_H[9,3] -2.860 0.737 -4.377 -2.859 -1.445
beta_H[10,3] 8.689 0.277 8.182 8.684 9.256
beta_H[11,3] 8.540 0.288 7.913 8.566 9.044
beta_H[12,3] 5.250 0.325 4.477 5.294 5.800
beta_H[13,3] 8.841 0.174 8.489 8.846 9.162
beta_H[14,3] 5.710 0.280 5.094 5.734 6.204
beta_H[15,3] 10.365 0.321 9.757 10.361 11.006
beta_H[16,3] 6.222 0.613 4.870 6.277 7.262
beta_H[1,4] 8.277 0.176 7.897 8.286 8.592
beta_H[2,4] 10.130 0.121 9.875 10.137 10.348
beta_H[3,4] 10.121 0.164 9.767 10.133 10.407
beta_H[4,4] 11.805 0.442 10.954 11.814 12.678
beta_H[5,4] 5.447 0.753 4.227 5.374 7.209
beta_H[6,4] 7.039 0.909 4.982 7.299 8.288
beta_H[7,4] 8.211 0.354 7.488 8.215 8.901
beta_H[8,4] 6.715 0.266 6.264 6.727 7.133
beta_H[9,4] 7.189 0.483 6.222 7.192 8.159
beta_H[10,4] 7.766 0.236 7.305 7.768 8.243
beta_H[11,4] 9.387 0.202 8.992 9.388 9.796
beta_H[12,4] 7.145 0.215 6.737 7.143 7.591
beta_H[13,4] 9.049 0.143 8.766 9.050 9.317
beta_H[14,4] 7.731 0.225 7.317 7.726 8.196
beta_H[15,4] 9.470 0.237 8.991 9.469 9.919
beta_H[16,4] 9.358 0.241 8.920 9.348 9.863
beta_H[1,5] 8.979 0.144 8.690 8.985 9.257
beta_H[2,5] 10.780 0.095 10.600 10.781 10.972
beta_H[3,5] 10.933 0.170 10.620 10.927 11.294
beta_H[4,5] 8.387 0.451 7.511 8.378 9.309
beta_H[5,5] 5.405 0.567 4.084 5.459 6.402
beta_H[6,5] 8.809 0.626 7.913 8.669 10.236
beta_H[7,5] 6.811 0.344 6.135 6.811 7.505
beta_H[8,5] 8.222 0.220 7.871 8.206 8.642
beta_H[9,5] 8.217 0.481 7.267 8.203 9.162
beta_H[10,5] 10.084 0.226 9.633 10.087 10.536
beta_H[11,5] 11.508 0.228 11.055 11.508 11.953
beta_H[12,5] 8.485 0.197 8.094 8.478 8.875
beta_H[13,5] 10.012 0.133 9.759 10.009 10.285
beta_H[14,5] 9.197 0.232 8.753 9.188 9.672
beta_H[15,5] 11.162 0.246 10.680 11.163 11.647
beta_H[16,5] 9.917 0.178 9.556 9.921 10.256
beta_H[1,6] 10.181 0.195 9.844 10.161 10.616
beta_H[2,6] 11.516 0.109 11.302 11.515 11.740
beta_H[3,6] 10.806 0.164 10.436 10.817 11.103
beta_H[4,6] 12.870 0.785 11.245 12.886 14.383
beta_H[5,6] 5.907 0.602 4.797 5.882 7.139
beta_H[6,6] 8.778 0.678 7.023 8.904 9.731
beta_H[7,6] 9.822 0.565 8.725 9.818 10.974
beta_H[8,6] 9.521 0.293 9.004 9.537 9.980
beta_H[9,6] 8.461 0.788 6.932 8.435 10.129
beta_H[10,6] 9.513 0.307 8.879 9.534 10.066
beta_H[11,6] 10.813 0.351 10.065 10.832 11.441
beta_H[12,6] 9.365 0.249 8.878 9.360 9.885
beta_H[13,6] 11.048 0.171 10.753 11.037 11.383
beta_H[14,6] 9.836 0.296 9.245 9.840 10.431
beta_H[15,6] 10.845 0.431 9.991 10.847 11.681
beta_H[16,6] 10.538 0.237 10.032 10.553 10.990
beta_H[1,7] 10.861 0.891 8.691 10.980 12.225
beta_H[2,7] 12.207 0.438 11.310 12.225 13.025
beta_H[3,7] 10.515 0.677 9.058 10.566 11.677
beta_H[4,7] 2.544 3.999 -5.024 2.467 10.782
beta_H[5,7] 6.448 1.818 3.181 6.390 10.510
beta_H[6,7] 9.567 2.486 4.856 9.568 15.980
beta_H[7,7] 10.674 2.824 5.118 10.713 15.993
beta_H[8,7] 10.993 1.099 9.464 10.917 12.692
beta_H[9,7] 4.382 4.008 -3.907 4.549 11.968
beta_H[10,7] 9.815 1.405 7.214 9.718 12.897
beta_H[11,7] 11.006 1.722 7.890 10.885 14.790
beta_H[12,7] 9.974 0.930 7.942 10.065 11.509
beta_H[13,7] 11.654 0.776 9.973 11.749 12.881
beta_H[14,7] 10.397 0.959 8.377 10.454 12.152
beta_H[15,7] 11.940 2.238 7.471 11.955 16.463
beta_H[16,7] 12.353 1.287 10.277 12.204 15.213
beta0_H[1] 8.554 13.013 -18.345 8.551 34.273
beta0_H[2] 10.957 6.250 -0.717 10.917 23.754
beta0_H[3] 9.852 10.312 -12.798 9.995 30.225
beta0_H[4] 6.429 185.265 -364.060 5.054 372.359
beta0_H[5] 4.420 24.258 -44.121 4.543 53.372
beta0_H[6] 7.232 53.718 -108.810 7.614 111.465
beta0_H[7] 4.497 133.970 -263.395 3.328 280.959
beta0_H[8] 6.535 44.478 -14.800 6.687 24.484
beta0_H[9] 5.922 121.868 -246.246 8.268 253.328
beta0_H[10] 8.291 31.724 -56.122 8.404 76.342
beta0_H[11] 11.280 48.334 -91.790 10.804 118.865
beta0_H[12] 6.519 11.234 -15.925 6.628 28.979
beta0_H[13] 9.470 11.445 -11.840 9.556 30.064
beta0_H[14] 7.171 11.094 -14.470 7.207 28.456
beta0_H[15] 10.389 110.449 -215.822 9.506 238.921
beta0_H[16] 7.557 25.947 -45.079 7.647 61.658